SOLUTION: Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following: 1. What is r, the ratio between 2 consecutive terms? 2. Using the formula for the nth term of a geo

Algebra ->  Radicals -> SOLUTION: Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following: 1. What is r, the ratio between 2 consecutive terms? 2. Using the formula for the nth term of a geo      Log On


   

Question 34410This question is from textbook College Algebra
: Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:
1. What is r, the ratio between 2 consecutive terms?

2. Using the formula for the nth term of a geometric sequence, what is the 24th term?
3. Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?

All help is greatly appreicated!!!!!!! This question is from textbook College Algebra

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
a geometric sequence is one that has a common factor (ie a multiplier) between terms. Just looking at the sequence... start at 1. What do we multiply it by to get to next number, 2. Answer is 2... r=2.

If you have a more awkward sequence, then divide one term by the previous one: 8/4 is 2. 4/2 is 2. 2/1 is 2 etc.

24th term:
1st term is a
2nd term is ar
3rd term is ar^2
4th term is ar^3
...
24th term is ar^23

So, +ar%5E23+
+%281%29%282%29%5E23+
+2%5E23+
work it out yourself :-)

sum of 10 = +%28a%28r%5E%28n%29-1%29%29%2F%28r-1%29+
sum of 10 = +%28%281%29%282%5E%2810%29-1%29%29%2F%282-1%29+
sum of 10 = +%282%5E%2810%29-1%29%2F%281%29+
sum of 10 = +1024-1+
sum of 10 = 1023

jon.